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The fundamental solutions to the Cauchy problem as well as to the source problem are considered for fractional heat conduction in two joint half-lines under conditions of nonperfect thermal contact. The specific example of classical heat conduction is also investigated.<\/jats:p>","DOI":"10.3390\/e27090965","type":"journal-article","created":{"date-parts":[[2025,9,17]],"date-time":"2025-09-17T05:59:51Z","timestamp":1758088791000},"page":"965","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Fundamental Solutions to Fractional Heat Conduction in Two Joint Half-Lines Under Conditions of Nonperfect Thermal Contact"],"prefix":"10.3390","volume":"27","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7492-5394","authenticated-orcid":false,"given":"Yuriy","family":"Povstenko","sequence":"first","affiliation":[{"name":"Department of Mathematics and Computer Sciences, Faculty of Science and Technology, Jan Dlugosz University in Czestochowa, al. Armii Krajowej 13\/15, 42-200 Czestochowa, Poland"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1630-7958","authenticated-orcid":false,"given":"Tamara","family":"Kyrylych","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Computer Sciences, Faculty of Science and Technology, Jan Dlugosz University in Czestochowa, al. 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